{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "836adb2a",
   "metadata": {},
   "source": [
    "# Post-training calibration\n",
    "\n",
    "Consider the case where an additional dataset is obtained after the training/sampling is complete. Instead of combining the training and additional dataset together to perform training/sampling again, which may not be ideal for some reasons, e.g., fitting a model is extremely computationally expensive, we can do calibrations.\n",
    "\n",
    "In this jupyter notebook, we focus on regression task on $$y = x + 1.5 \\sin(4\\pi x)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a5b24e88",
   "metadata": {},
   "outputs": [],
   "source": [
    "import neuraluq as neuq\n",
    "import neuraluq.variables as neuq_vars\n",
    "from neuraluq.config import tf\n",
    "\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "375aa3f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data():\n",
    "    data = sio.loadmat(\"../../dataset/calibration.mat\")\n",
    "    x_test, u_test = data[\"x_test\"], data[\"u_test\"]\n",
    "    x_train, u_train = data[\"x_train\"], data[\"u_train\"]\n",
    "    x_cal, u_cal = data[\"x_cal\"], data[\"u_cal\"]\n",
    "    return x_train, u_train, x_cal, u_cal, x_test, u_test\n",
    "\n",
    "\n",
    "x_train, u_train, x_cal, u_cal, x_test, u_test = load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12cb4031",
   "metadata": {},
   "source": [
    "#### Training\n",
    "\n",
    "First, suppose we don't have calibration data, we use a BNN with one-hidden layer to approximate the training data. As shown below, the BNN fits the data well, but the uncertainty estimate is bad: the uncertainty does not bound the error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d029b92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supporting backend tensorflow.compat.v1\n",
      "\n",
      "Compiling a MCMC method\n",
      "\n",
      "sampling from posterior distribution ...\n",
      "\n",
      "Finished sampling from posterior distribution ...\n",
      "\n",
      "0.647\n"
     ]
    }
   ],
   "source": [
    "process = neuq.process.Process(\n",
    "    surrogate=neuq.surrogates.FNN(layers=[1, 50, 1]),\n",
    "    prior=neuq.variables.fnn.Samplable(layers=[1, 50, 1], mean=0, sigma=1),\n",
    ")\n",
    "likelihood = neuq.likelihoods.Normal(\n",
    "    inputs=x_train,\n",
    "    targets=u_train,\n",
    "    processes=[process],\n",
    "    sigma=0.1,\n",
    ")\n",
    "model = neuq.models.Model(\n",
    "    processes=[process], likelihoods=[likelihood],\n",
    ")\n",
    "\n",
    "method = neuq.inferences.HMC(\n",
    "    num_samples=1000,\n",
    "    num_burnin=1000,\n",
    "    init_time_step=0.1,\n",
    "    leapfrog_step=50,\n",
    "    seed=None,\n",
    ")\n",
    "model.compile(method)\n",
    "\n",
    "samples, results = model.run()\n",
    "print(np.mean(results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d59112ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred, = model.predict(\n",
    "    x_test.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0)\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_train, u_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11ecf6ff",
   "metadata": {},
   "source": [
    "#### Calibrations\n",
    "\n",
    "Now we use the additional dataset to calibrate the uncertainty. As shown below, the uncertainty is calibrated such that it is able to bound the error, even for region where neither training data nor calibration data is presented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1cce9613",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:  0 , loss:  55.761555\n",
      "Iteration:  2000 , loss:  11.52133\n",
      "Iteration:  4000 , loss:  10.690694\n",
      "Iteration:  6000 , loss:  10.687571\n",
      "Iteration:  8000 , loss:  10.687571\n",
      "Iteration:  10000 , loss:  10.68757\n",
      "Iteration:  12000 , loss:  10.68757\n",
      "Iteration:  14000 , loss:  10.687571\n",
      "Iteration:  16000 , loss:  10.687571\n",
      "Iteration:  18000 , loss:  10.687571\n"
     ]
    }
   ],
   "source": [
    "u_pred, = model.predict(\n",
    "    x_cal.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "\n",
    "calibration_model = neuq.calibrations.CalibrationVar(\n",
    "    targets=tf.constant(u_cal, tf.float32),\n",
    "    predictions=tf.reduce_mean(u_pred, axis=0),\n",
    "    stds=tf.math.reduce_std(u_pred, axis=0),\n",
    "    optimizer=tf.train.AdamOptimizer(1e-3),\n",
    ")\n",
    "s = calibration_model.calibrate(num_iterations=20000, sess=model.sess, display_every=2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e00c20ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred, = model.predict(\n",
    "    x_test.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0) * s\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_train, u_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.plot(x_cal, u_cal, '+', label='calibration')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0c30389",
   "metadata": {},
   "source": [
    "#### What if calibration data is used for training?\n",
    "\n",
    "A natural question is: is calibration necessary? What happens if we use the calibration data for training as well? As shown below, the predicted mean is of course more accurate, which is certain because we have more data. But uncertainy for region without any data is still bad. The predicted uncertainty here indicates that we should trust the prediction for region where there is no data, which is clearly wrong. $\\textbf{In terms of uncertainty}$, for the same model we use so far, using the additional dataset for calibration is clearly a better choice, than using it for training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "afe80dcb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling a MCMC method\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x_new_train = np.concatenate([x_train, x_cal], axis=0)\n",
    "u_new_train = np.concatenate([u_train, u_cal], axis=0)\n",
    "likelihood = neuq.likelihoods.Normal(\n",
    "    inputs=x_new_train,\n",
    "    targets=u_new_train,\n",
    "    processes=[process],\n",
    "    sigma=0.1,\n",
    ")\n",
    "model.likelihoods = [likelihood]\n",
    "model.compile(method)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "68433afd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sampling from posterior distribution ...\n",
      "\n",
      "Finished sampling from posterior distribution ...\n",
      "\n",
      "0.537\n"
     ]
    }
   ],
   "source": [
    "samples, results = model.run()\n",
    "print(np.mean(results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1c3328e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAD8CAYAAABq6S8VAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAABa5klEQVR4nO29Z3ic1bWwfe8pmhmNRr03S7JcJcsFdxswtsGm2RRjTIADKZByCDl8SQgJgRCSk5NzkjfkQMJLeBMgEJqpMRgCuHcbV7nbkq3e26iMpGn7+zGykWxJlqwpKvu+Ll2aecrea56ZWbOetVcRUkoUCoVCMXTRBFoAhUKhUAwMpcgVCoViiKMUuUKhUAxxlCJXKBSKIY5S5AqFQjHEUYpcoVAohjheU+RCCK0Q4oAQ4mNvjalQKBSKS+NNi/wHwHEvjqdQKBSKPuAVRS6ESAZuBP7qjfEUCoVC0Xd0Xhrnj8CjgKWnA4QQDwIPApjN5ivGjx/vpakVCoViZLBv374aKWXMhdsHrMiFEDcBVVLKfUKIBT0dJ6V8EXgRYPr06XLv3r0DnVqhUChGFEKIwu62e8O1Mg9YJoQoAN4CFgoh/uGFcRUKhULRBwasyKWUP5VSJksp04BVwAYp5T0DlkyhUCgUfWLIxZG32l2BFkGhUCgGFV5V5FLKTVLKm7w55oVUN7X7cniFQqEYcgw5i7y6uR1VQ12hUCi+YsgpcrvTjbXVEWgxFAqFYtAw5BQ5KPeKQqFQdEYpcoVCoRjiDElFbrO7aG53BloMhUKhGBQMSUUOUNXYFmgRFAqFYlAwZBW5cq8oFAqFhyGryJvanLQ5VHKQQqFQDFlFDsoqVygUChjiirxKKXKFQqEY2oq8wWbH4XIHWgyFQqEIKENakUsJNc3KKlcoFCObIa3IQfnJFQqFYsgr8toWO263KqKlUChGLkNekbtckjqbPdBiKBQKRcAY8ooclHtFoVCMbIaNIlc1yhUKxUhlWChyu9NNY6sqoqVQKEYmA1bkQgijEGKPEOKQEOKoEOKX3hCsv1SrMESFQjFC8YZF3g4slFJOBqYAS4UQs70wbr9QfnKFQjFSGbAilx6aO57qO/787rBuaXdisyv3ikKhGHl4xUcuhNAKIQ4CVcAXUsrd3hi3v9Q0qTBEhUIx8vCKIpdSuqSUU4BkYKYQIvvCY4QQDwoh9goh9lZXV3tj2ouoblbNJhQKxcjDq1ErUsoGYCOwtJt9L0opp0spp8fExFzW+K/uLOCP6071uL/B5lBFtBQKxYjDG1ErMUKI8I7HJuBa4MRAx+2ONoeL3WfrKGto7Xa/KqKlUChGIt6wyBOAjUKIXOBLPD7yj70w7kXcPi0ZrUaw5XTPrhnlJ1coFCMN3UAHkFLmAlO9IMsliQoxMDMtkh35tdw+LRm99uLfoZqWdtxuiUYj/CGSQqFQBJwhl9m5cHwsNruLfYX13e5XRbQUCsVIY8gp8omJocRYDL27V5SfXKFQjCCGnCLXCMFVY6I5VdlMubX7RU/lJ1coFCOJIafIAeaOjkYrBFtO13S7v83hoqnN4WepFAqFIjAMSUUeZtIzJSWcnfm1PcaNq9orCoVipDAkFTnAlWOiaW53crC4odv9Nc3KvaJQKEYGQ1aRT0wIJdIcxNYe3CuNrQ7aHC4/S6VQKBT+Z8gqco1GMD8zmmPljT26UVT0ikKhGAkMWUUOMG90FALYnt+9Va7cKwqFYiQwpBV5VIiBrMRQtufV4HZfXAK9rqUdVzfbFQqFYjgxpBU5wJVjYqi3OThSZr1on9sNtS3KvaJQKIY3Q16RT04Ow2LUsTWvB/eKSg5SKBTDnCGvyHVaDXMzosgttmJtvTgJqKa5HSmVe0WhUAxfhrwiB5iXGY1LSnadqb1on93pprFN9fJUKBTDl2GhyBPDTYyOMbMtr6Zb61tleSoUiuHMsFDkAPMzoym3tnGmpuWifSqeXKFQDGeGjSKfkRZJkE7D9m4WPZvbnCrLU6EYpLjckgabHbuzm7pJuavhmWx4KtzzP3e13+UbCgy4Q9BgwajXMn1UBHsK6rhzegoGvbbL/uqmdlIigwMknUKh6I6qpjZOVTRjs9ux2mtodFWREhbBtZnTEIffgY8eBkdHuWprsec5QM7KwAk9CBk2ihw87pUd+bXsLapn3ujoLvtqmpUiVygGC06Xm8OlVqqbWnm38Dl213yKW35113xd0R38Z+7bGB0X9BxwtML6p5Uiv4ABK3IhRArwKhAHSOBFKeX/DnTcy2FMbAhxFgPb82ouUuT1NjtOlxtdN30+FQqFfzlV2UxVo43Xz/43B+o2MiNqCemWiUQExXGsYRefl7xDgdnJ/9h0jHZcEHVmLQmM0IMYb1jkTuCHUsr9QggLsE8I8YWU8pgXxu4XQgjmZUbz/oFSKhvbiAs1nt/ndkOdzU6sxdjLCAqFwqfkrsb1xS/JbCrlhYQkDhg1BDcvY8PxuYSZ9ESZg8iIWcb96dP4Z/4T3J0Yz7ul5SQ7O61xhSUHTv5ByoDNUylluZRyf8fjJuA4kDTQcS+XOaOjEAJ25F8cU67CEBWKAJK7GvnRw2ibSvhldAQbjRoeqWlkQbXghux4JiWFEaTTsP54Fe/vCOOHlnsA+EV0FOeXQfUmWPRkwF7CYMWrPnIhRBowFdjdzb4HgQcBUlNTvTltFyKCg8hKCGVHfg3LJyei0Yjz+2qb7UgpEUL0MoJCofAJ659GOFo5aAhijSWEbzZY+UaTFZvpXXZM+/75w46WWXlxyxkeOzSFlWMLeV+zjbctFu7ShHuUuPKPX4TXHMZCiBDgPeA/pJSNF+6XUr4opZwupZweExNz2fPEWIIuecy8zGjqbQ6OV3QVQ2V5KhSBQ1pLcAP/ExlBjNPJgw2e76eptaLLcVmJYTxx00RiLAZeO3YjKcYp/D42gfz7P1FKvAe8osiFEHo8Svx1KeX73hizJ0ZFmdFpe7eop6SEExykVe4VhWIQ4TAn8ok5mMNGAw/XWwnuyMJuC04gKiSIUJMeo16LEBAdYuDH140jKsRIed7NCDT8bOsTqm5SDwxYkQuPn+JvwHEp5R8GLlLv6LUa0qPNlzxmZlok+4vqsdm7WuAqy1Oh8D82u5ODEx/imcgIJrTbWdbsycB2aU1oFv+CqakRzEyPZP6YaGakR2IK0mIK0vLtqzJoagnBYlvOsfr9fHZmU2BfyCDFGxb5POBeYKEQ4mDH3w1eGLdHUiKCMV6Q8HORUJnROFySLwvqu2xXWZ4Khf8prmvlPxuqqNJpeahRIBA4Lclolj+LYdqqLseGGvXMTI8kNtRAWpSZO65I5uzZLAwigr8dfllZ5d0w4MVOKeU2wK+rhxqNYHSsmaOlF7niz5MWFUximJEd+TVcPbarT76muZ3kCJUcpFD4A4fLzYmKWvLbPyVETsZ+w/8hLyqYMXGWHs/RazXkJIdzqrKJheNjOVHZxLHKuZyQa9lSuJ+r067w4ysY/AzZ7Jj4UCMhxp5/h87FlOdXt1Bu7ZodpvzkCp+haoNcRFlDK++cWIvQ2rgueQXBBi0ZMSF9OjczJoQIcxD/NnsUmqbZCGnkpSMvqxaOFzBkFbkQgtGX+DDMzvDElO+8YNGz3mZXHwSF9+mIk8ZaDMivaoOMYGUupaSwxkZu47/QOmO5KmU2WQlhaDV9u4nXaATZSWFEhhi4ITuNttpZHKjdyu7iUz6WfGgxZBU5QIzFQHiwvsf9YSY92Ylh7DxT26U5s+rlqfA2brfE+cUvET3VBhmh1LXY+fTUPqShgMlhS0mLNhPWy3e2O4x6LdmJoSyeEEdI+wKkFLx27FWcrm6qJY5QhrQiB8iM7d0qnzs6inqbgxMVTV22q16eCm/R5nCxI78WbVMpAHZgY7CJx2KiuCsxjvdd9TjdIzN/obKxnQ1la0DqWDnhVjKi++ZSuZCoEAOjY0NYMTkLu3UqO6v+xfGqikufOEIY8oo8PDiIqJCek4TOxZRvz+9ap7y2RfXyVAwcKSVHSq20OVy0BSfwkTmYq0cl83BcDNtMRtqE4BcxkSz7cBlrz6wdUZ85t1uy42wJLfrdJOpmkxWX0CXTur+kR5uZMzqSOPdiXNh558Qa5SLtYMgrcoDRvVjleq2GGWmRHChqoNX+Vdhhu0NleSoGTn51Cw02B42tDn4buoQnYqIYY7fzfyuq2FhUyltlDfww9CakO4jHtj7Gu6ffDbTIfqPeZufdEx8jtHaWZ6wgKcI0oPH0Wg2jYyysmjILV1sCG0o+pbS+9dInjgCGhSIPNeq7VDq8kLmjo7C73Owr7BpTrpKDFAOhtrmdgpoWdp2p5acfr+e9oO2EusP4rzoN81rbqSGaH7d/g+2Nt/Mf459nUuRMfrv7txyr9Xth0IBQWGuj2LkBk0xhQdp09F4oIZ0cYWJKSjjhrrlY3WfYVnSky/rXSGVYKHKAjBgzPdXCyog2E2cxsONMV/dKjQpDVFwmLrfkaFkjpfWt/H33UUwpr2AOMvDvU//M8eVbWL/yJEfu2E7z2Nv44ngl7+4v446URwkzhPPDTT+k0d5zDsRwQErJh0cOoTGWMjl8EalRvWdj9xWNRpAZG8KN6TcgpYb3T31IaYOyyoeNIjcbdD1a5UII5mZGc6qyuUsMeZPK8lRcJmUNrTS3OfnL1nyM8R+BzsoDY39FlCHh/DFCCO6akcLCcbF8cayST3ObuDfj51S0VPDEtuFdN6Suxc7WsvUArBh/IyEG7xVajQ01ct340ejbJ3CqZQtnahqH9bXsC8NGkUPvVvmcjCgEsOtM15jy2hYVvaLoH1JKiupsrN5bTEVrAYQc5Jr4FYwJz2ZcvIX5Y6KZlBxGYriJIL2Wu2amcM24GD4/Vkl5ZTx3j/0uG4o38FnhZ4F+KT6jqM5GlXsPZpnBFcnpXh8/PSaEWdHXIbVWPji+acQn+Q0rRR4cpCMhrPsFlUhzEOPiLew4U9vl13ukfwAU/ae6qZ0deTVsOlVNSsYWjFoT9064j7mjo0iJ9NQBigs1MjExlFnpkQQbdNw1I5W0qGDe/LKI0UFLGWVJ4y+H/oJbDr9YaCklHxw5hMZYxtTIBUSZL116ur9Ehxi4M3spuExsq/iMgtoWr88xlBhWihw8Vrmmh1c1Z3QU1U3t5Fd/9abXt6gsT0X/OFPTwrv7S4iPrqGO/dw46k6mpSR1u5hn1Gu5YlQEIUYd/zY7jZZ2J+/vL2dJ0j3kNeSxvmh9AF6Bb2mwOdjW4Va5Z9JNPmvkMi4ugjTjPNqCDrH9TAkNtpF7dz3sFLlRryUxvHur/IrUCIJ0GnZ2cq+43JI65V5R9JEGm53teTVUNrYTlriBYJ2FH0z/Zq/nGPVapo2KYHyChWsnxrE1rwbRMoVUyyheOPTCsLPKyxpsVLr2ECwzmJSQ5rN54kONLMu8GaFx8En+egprbT6ba7Az7BQ5QFpU91a5Ua9lWmo4XxbU4eiU3qvCEPvBCC8KVVhr4/OjlYSHl1Hm2M+94+8jwhR2yfOMei3ZyWEsn5xIdEgQ/9hVwrWJd3Oq/hQbizb6QXL/8f6R3A63ytWEGvuXjt8fNBrBovSZBBFJiX03pyubLuo/MFIYloq8N6t8TkYUNruLQyUN57cpRd5Hcld7ikCN0KJQbQ4XewvqOFnZRFTydkKDwvlGzr19Pj/UqGdsvIW7Z42iorGNitIJJIek8ELuC8Mm6qLN4WJj8TrA41bxNSmRwUyJvBKt+RTrTxaNWKt8WCpy6NkqnxAfSrhJ36UioifL0+FH6YYo65/2FIHqzAgqClXV2M7nxyoxGluocR3gtjG3EqzvX1379OgQZqRFMCY2hM+OVnFt4t2cqDvBttJtPpLav1Q2tlHl2k2wO4NJ8d6PVrkQvVbDsszrERon28u3UlJv63K3PVIYtoq8J6tcoxHMzojiSGkjja1fKW+VHNQ7TreTo62VtHa3cGUt8b9AAeBYuZW9BfWMTj+JGze3jrml32NoNYKJiWHcnJNIvc1BdflEwg0RvHf6Pe8LHAA+PX4cYSwjO2IeYSbfuVU6syBtOiZNBHbDQfYW1I/ItP1hq8ihZ6t8zugoXFKyp6Du/LaaZrXg2R1SSjYVb+L2NbezKimeK1OT+F5cDO9azJz/GQxLDqCE/qHN4eLDA2W4cWML2smUmClkhGVc1liR5iCuGR/D6BgzIvd9bqqvZXPhOmr+OLTXHKSUfHbG4+9fMf46v80bZjIwO24B+pBTrDtRTHG9bcSl7XtFkQshXhJCVAkhjnhjPG/Rk1WeFG4iNTK4S/RKY6tDZXleQHFjGXeuuY/vb/g+ze12HghdxIqWNs7qdfwyOorHY6Jw602w6MlAi+pzKqxt7DxTy7jUemrsxdw25rYBjZcZa+FHCYf4uXyBO+oqcArBWnfDkF5zaGx1UtC6F60rmjmpE/069w0ZS0DjoLB1H3lVzVSPsHUvb1nkrwBLvTSWV0mL6j7bc3ZGJIW1Nso61WlQWZ5f0dTWzsPrf8yZxhPcPur7PJr1VyaO+yk3jn6MD+s1fL+ugU9DzPxh2s2QszLQ4vqcLaersbY6MEbsxaQzcV3awCxOU5CWRWV/IVjYyXA4mdzWzvuWEOQQXnPILavCEXSKFON0woO9nwTUG9eMmkmILgJ96GG2nq6hqG5wLnr6alHbK4pcSrkFqLvkgQHAqNd2m+05K93TBq5zyr7yk3toanPw6+3PkdeYyx1p/8H82OUItLQ7XFSOWsbWGzcy4cb9rBx7J3+v2sWrR18NtMg+pdXuYtOJavQ6ByXOnSxJW4JZP/AiUPrmsvOPb2tq5kyQnkOGoCG75vDO0U0IjZPFoxb4fW6DXs+c+AXoLSfZdbacmqZ2rLbBFcBQ3FjM4ncXs7t8t9fH9puPXAjxoBBirxBib3V1tb+mBSAtOvgiqzzMpCcrIZRdZ+twd/xK1qksT5wuN+8e3cKnJa8xznwNG/cl85P3cvnu6/t56M0D/GNXITa7k3anm6UJ32Fx6mJ+t/d37CjdEWjRfUPuanTPTuKvhdfyRMRjtLtauTXzVq8MLTqtLSxpsWFyu/nAEjIk1xzsTjf7q3eA28CKrKsCIsONo69DCjv2oOPsL6qnuH5wWeVbS7dSZasi0Zzo9bH9psillC9KKadLKafHxMT4a1rAU4Olu8qIc0ZHUddi51Slpw2cyvKEw+XlvHTqP7FoY8k9dA2VjW1kxoawJCuOq8bGsPl0NU/88yh7C+uw2lw8MP5xUi2p/G7v73C5h9kaQ0fcvL65FA2SzWYXoxxOplac9s74i55E6jx3i2YpWdpi41/mYGwLHvPO+H6kqqmVBnGIMLKID728dm4D5erU2Zh1oZgjTrDtdA2VjW2Dat1rW+k2Ui2ppISmeH3sYR210pn06ItvhaekhGPUa9h1pnP0ysh1r7Q5XLx09K9Y7bVU5d9BbEgYP79xIg9cmcFt05K5d/YoHr9+AmEmPS9sPsMXxyopq3dx/4TvkteQx8dnPg70S/AuneLm6zUa9hoNLGluQWz4lXfGz1mJWPYs7eYk3FJwTYsem0bD55bAKMKB8OHRvQidlSlRc9AOoJ3bQNBpdMyOn4/GfIzjFQ1UNbZTMkhCEdtd7XxZ8SXzk+b7ZPwRo8i7q1du0GmZlhrBvsJ67E5PEsFIVuQHSkrZVvkxdutkUkPG8uPrxl0UC5wWbebxGyYwNSWcd/YVc6KikRjNTLKisvjTwT/R7hpG16+Tr3pjsAm3ECy22bzrw85Zif37h3gw4wu+1fAMkYZ4PisYeuVtvyj0hB2uyvZf2GF3XJ9xLU5s6Mxn2J5XQ2lD66AIRdxbsZc2V9vgVuRCiDeBncA4IUSJEKL3KkIBIi364iy8ORlRtDpcHCxuAEZulqfV5uDd02/jlG2EtV/HI4vHYjboCDHqSAg3Mjo2hLFxFoJ0GrQawTfnpxMXauSFzWeotLZx5+jvUNFSwVsn3gr0S/EenXzV68zBJDmcjLc7vO7Dthj13DI1EbeEEMc0dpbtwtpu9eocvqTV7qKodS86xyimJKUGVJarUuYRpDEQG5/H9vwa2u0uKhrbAioTeNwqBq2BGfEzfDK+t6JW7pJSJkgp9VLKZCnl37wxrrexGPVEWwxdto2LtxARrO8SvTISa5QfKa9iY/n7OJsmcNeUmRj1WuLDjMxKjyQrMYz0aDOpUcHM6ai5bQrS8u8LMnG5Jc9vzsfkGsechHm8mPvisGlj5l74JO3CQJMQ7DIZWWyzIXwUNz8zPYrspDCKisfikk42FG3w+hw+IXc1jc9NwqUr4F5bPiEn3w+oOCadielxc3AZD1Nva+dImZXiQRCKuK10G9Pjp2PU9dxbeCCMGNfKOdKiulrlGiGYlR7FkTLr+ZT9kRaG2Nzu5J/5H+CgmSRxI9lJnu42WYmhF9WS1ms1jIu3MDU1goRwI9+cn05hrY01h8pYlvItGu2NvHH8jQC9Eu/SMHo5T8lvs9Ych0MIFgsL3PysT+LmY0IMXJ8dT1NjHCHaOP5V8C+vz+F1OhaD97jrkUKwpLkm8AlNuau54fQGbO46Xg79/9AceYemNmdAa5UXNxVT0FjAlUlX+myOEafIw4ODiDB39fvOyYjCLeHLjpT9kdbLs7CukfXlq3HZ0rl3ytUkRZiYkGDptSHAuY5LU1LCmZUeyedHK2lpimVm3BzePfUuTvfQLye6t7CON9tm8/ekK4k2RZPzUK7Pkp+EECzNjicmxIhszmFX+W4a2hp8MpfX6FgM3h5sItLlYoLdHtgiah0/LAtqy9BKSa65nQet/0t43ocU1wVu0fNcQTRf+cdhBCpy8GR7diYpwkRKhKlLyv5Ica+4D63m6Op52Knnd80nmdWynnFxvSvxcyRHBJMUYeL2aclohOC9/aXMjL6RSlvlsKjmt+lkDQg7Vc5DLEpdhEb49uuSHBHMVWOjqSofj1u6Bn/3IGsJbmCHycjc1ravlEmgEpo6fljC3G6mt7WzPjiYYGFn9OH/Q1VT4EIRt5VuI8WSwqjQUT6bY0Qq8mCjm921/2Rzxfvsr93A6caDzMoIo6DWRoXVszAyIqJXOiyYTwxO0uwObmipYOyex9EceafPQ4yLs5ARY2ZJVhx7CupwNU0g2hjD6pNDs17IOdocLvYV1hMXV4jd3cai1EU+nzNIp+HWqclgT8RILJ+eHeTulbBkjgUFUa/VMs/W2mV7QOj0A7KwxcbZID1n9DrCHFVISUBCEdtd7ewp3+NTaxxGoCIvsBZw9yd389aZ5/iw+HleO/Mbnj/5I06JZxDa9vOLnvU2O87hXtd4/dOUY2efycjNzS0IQOPs362xRiPISgzjhknxhJv0rN5byry4G9lWuo3S5lLfye5jiups5FU1Y4k8TpghjOnx0/0yb05KGJOTI2hrmMSXlV9S1zYoK194WPQkm80hCCmZ29oRGRLIImqdfkAWdvywbAgOpswdRUVjW0BCEfdV7PNp2OE5RpQi/6zgM1atXUW1rZo/L/ozf5j5Tx7LfonbR32fwpbDRGb8jZ2FhbilxO2GumHezFVaS/g4xONmurGlUxfyft4am4K0jIkL5fZpyRTU2nBbZyKE4L1TQ7fG9qaTVbiki0bNYa5Ovhq9xj+1tUONepZkxdFSlzXo3Svu7Dt4P2QUY+xuItwSwlJ8thjcJxY96fkhAeJdLia1tfO52czvXCvZmV+Lw+n2eyjippJNGLVGZsbP9Ok8I0aRby7ezI82/4jM8Ezeufkdrkq+ignx8cSZUpkfu5xvjHkal66c1ujnOFhWAAx/P7kjJJGPzWauaG0jydnJf3gZt8ZpUcFcOTaapHATm47ZmRo1l/dOv4fDNfRi8qWU7MirxWQpodXVxJXJvos26I7rJyUQph2FzhXDv8584de5+0NRQxVV2jrqtcvhF/XwyJHAVsLMWen5IQlLAQSL3EEcN+g5ET+LnWdqcUvp11DEc7X85yTO8VnY4TlGhCJvcbTwq12/IjM8k5eWvES8OR6AxDATQTrPJcgKn823Mn+LRtfIhyV/QEpJTbN92PRS7I53Rq2kIEjPzc2drPHLvDXWaTWMjbNwfXY8ZdY2IlxXU9dWx/riwWtR9kSDzU5uiZWY2DNohZa5iXP9On9iuImrxsRga5jAvqovabI3+XX+vrL66AYQkplxc/u0OO4XclZ6flCeauDauz8BIC7hNHUtdk5WNPk1FPFU/SnKW8pZkLLA53ONCEX+7P5nqbJV8dTcpwjSflUnWaMRpEZ+FVc+PmIyCe5badIc50DtFhxON9bWoWdR9oXGNgcv2xrQuDVcKcMAMeBb44QwI4smxBEdEsTBU7FEGWP5OH/o1V85UNzgcasFH2dK7BRCg0L9Or9eq+HWaUk4m7JwSSebijb7df6+srl4G9IZzG1ZswMtSrekhqaSETqGevZ11FTyrH/5KxRxU/EmBIKrkn1fDXLYK/JD1Yd488SbrBq/iskxky/anxRhQqv9ypq4YdRtuNoSeK/weeyutmHrXimoaaLCtQuzeyqOB/bDUw0DvjUWQjA+3sKSifGcrWklJWgu28u2D6l0c4BNJ6sROiv1zkK/fAm7Y0pKOOMjssBpYe0gdK/YnU5K2w+is49jYmJEoMXpkSXp11LYcoycVMG+Ik9NJX+FIm4q3sSk6ElEm6J9PtewVuQOt4OndjxFbHAsP5j2g26P0Ws1JHdqBzcxIQJd/W3Y3LWsK39j2Cryl/Z/itC2MC9+CXEXlC0YCBHmIG7Iicdi1FFROh6n28m6wnVeG9/XOF1u9hbUERVzBoCrkgKjyMODg1g0Ph5700T2VOygzRn4eiGd2VmSi0vTSKppGiEGXaDF6ZFrRy1GIomKPU2bw82hkga/hCJW2ao4UnvEL24VGOaKfE3eGvIa8vjZrJ/12tElJTL4fJNmrUYwK3E6TutUNlS8Q2FjEc3tQz9LsTM2u5PdVevBFczdOdeh03r3YzAuPpRrJ8RxuiSMCH0in5z9xKvj+5KKxjZOVTZjDj9FgjmB0eGjAybLsslJ6Fon4ZBtbCzaHjA5uuO94561j4Wp/l0I7i+Z4Zkkh6RS6fqyS00lX4cibinZAqAU+UCRUvKP4/9gXMQ4rkm5ptdjjXptlxK3czKiaKu6HqSWf5W+Muys8vxqK02aw0RrppEWZfH6+NEhBm6anIBRr0XbOo0vK76k2ubfrlCXy9bTNTilgyZxnKuSrwroIl5qVDAzE2YiXUY+Oj24Stvur9mJqzWZ6yeOCbQovSKE4LpR15LfdIipo4I4UtpIU5vD56GIm4o3kRSSRGZ4ps/m6MywVeS7K3aT15DHPRPv6dOXcVSntP2UCBMJIbEEtc7hYP0WTtUMzR6KPfH6oQ0IbRuz46/yWZPcrMQw5o2OpqR4LBLJ54Wf+2Qeb7Mjvwa9+SwO2RYw//g5gnQaluWk4Gwez+7Krdidg2PhvbK5DqsrD4s7u8v3ZrByXdq1uHETEXMKl5TsLagH8Fkoos1hY1f5LhakLPCbITBsFfnrx14n0hjJ9enX9+n4EIOOqBCPUhNCMCcjiurS6bilm8+KPhg2RbTanS52VmxBuvX825RrfTZPrMVTzc/RFkuISGHtmcHvXml3ujhUbCUyJt+ntaP7w/wxMYTLqdhlM5sK9wRaHADWnt4EQjIxwlPueLAzMWoiCcFJFLRtJyncxK6zHveKr0IRd5bvpN3V7je3CgxTRV7UWMTmks2sHLcSg7bvC3mdrYtZ6VHgiCJaTGFn9VrKrMOjxnZ5Qyu18gBhZJMR7btoAyEEczKj+V7kPlbW5nO4JpfS/80ObInTS1BQbfNYaaYTTI+fjklnuvRJPiY6JIhrUq9CunWsPv5poMUB4NMzG3E7g1mS6Z+yBQNFCMGNGTdyuukgU9M15Fe3UNXkcasU+cAq/+zsZ4Qbwrki7gqvj90Tw1KRv3HiDbQaLXeOu7Nf50Wag7AYdecfj4u3YK2aTbOzgY/zB8eXaKCsPrwTobMyPfpKDDrfWlMJhR/xSNufuaPF4x//l7sh8PWqe2HzqSrQ12KTFT6tHd0fhBCsmJaB2zaGAzVbabUHduHd5XaR17QPaRvLlWPiAipLf1iWeRMSN0FhuQDs7ujTW93U7tW7bZvDxqaSTVw76lq/lXWAYajIm+xNfHD6A65Pu/6y4jfTOjVpnpMRRV1NKhH6FD4tege7c2i7V1xuyfrCDUip4d7JS30+n2bD0+jdbSQ7XWS3t7POHBzYetWXYNfZOkxhpwEGjSIHGB8fSlLQTOyijvVn9gVUlr3lh3GKJuJ0U4m1+Dbt3Jukh6WTGTae402bGBsXwu6zdUgpO0IRvWeVby7ZTKuztc8uXW/hrZ6dS4UQJ4UQeUKIx7wx5uXyyZlPsDlt3D3h7ss6P9ZiOO/3u2JUBEFaLSHtCyix5bGlaK83RfU7dS3tlDn2EuzKZGJ8gu8n7FR8a1FLK0cMBsq12sDVq+4Fm93J4VIrloh8UiwppIYGtvdkZ8wGHcvGLEZKDa8fWRvQshH/PLUeKQWzE+ag93LYqq+5KeNGSmynmZjaRkVj23m3Skl9Ky4vhSJ+cvYTYk2xfnWrgBcUuRBCC/wZuB6YCNwlhJg40HEvl0/OfkJmeCZZ0VmXdb4QX6XtG/VapqaGU1AwHpM2hNWnhnZj4bXHD0NQBVkRcwkO8kMSR6fiW4tbPF+aDWZT4OpV98LhEivVzc20604xL3FeoMW5iOU5Y9C0j+ZE4w5qWwJXlXNH2TbcbcksHpcRMBkul2WZNyLQ4Azeh1Yj2H3W415xuiTl1oEnCFnbrWwr3caS9CU+b0JyId6YbSaQJ6U8I6W0A28By70wbr+paKlgf9V+lqYNzG2QGG48n7Y/JyMKW7uWlKB57K3eSmN7szdEDQj/POVJ9V6V5afbvk5lRdOcTkbb7awzhwSuXnUvbDldjdZUgIt2v1c77AsJYSbGhMzBqa3k0xMHAyJDZXMNtY58dG0TmZYaHhAZBkJMcAw5UdM5bN1IdmIoe87WnU8K8kb9lfVF63G6ndyQfsOAx+ov3lDkSUBxp+clHdu6IIR4UAixVwixt7raN8kh/+roqDJQ/5SuU9r+hIRQQo06WmpzcLjbWTPIEjP6SqvdxdnWL9E5k5gzyk9JHJ3KikoEM5sF+wwGajJ9322nP0gp+bKgnuDwPPQaPdPjBl80hl6r4e5JHgVRt/1+5FPh8Ix/o4DW5q8HIRkdMoMwk2/yD3zNTaNvpK69gozkGhpaHZyq8lSWbGl3UjfAO51Pz35KiiWFrKjL8wYMBL/Z/1LKF6WU06WU02NiYnwyxydnPyE7Ktsr/s2UyGCE6EjZz4jidHEUEfp4Ph1C6eadOVBahlN/hlTTFYQa/beafq6saMnDpaxx/QwpJB+dHly1V+ptdo6XN2KwnGJ63HSC9cGXPikAXNd+iOw2OztMLgQSrMV+jQL6JH8dbkcYV4+agkYzSMrW9pMbM65FrzFg1W3HoNOcj16BgYUi1rTWsKdiD9enXx+QbGBvKPJSIKXT8+SObX6lwFrA8brjXlst7py2PycjCpcbosVsDtftpaplaKSbd+btwxsQws2S9KsDMn9ieDALM6bgtofzUd7guqvZc7aOZmcN7Zpy5iUNPv/4OUK2/YbFthaOnVs0Br9FAbXYbZxu2o+zKYvFE+N9Pp+vsBgsXJlwHQfrN5KTqmdfUT2OjpaONU3t2C4zvPOTM5/glu6AuFXAO4r8S2CMECJdCBEErALWeGHcfvFpwacIBEvSlnhtzNQoj2WWEmEiKdxETUUWEjcfnFrrtTn8gdst2V+9E9xGVmQFRlFpNYLbpiXjbplEXtMBqpobAiJHd2w9XYMu5CSAz3srDghrCYtaPL7c9ebgLtt9zRdnt+LGTpz2CtKjB39afm98bcLXcLjbsUTvx2Z3caT0qzLLl+Mrd7ldvHXyLabETAlYkbUBK3IppRN4CPgMOA6sllIeHei4/ZSBT89+yhVxVxBn9l6SQqhRT4RZjxCCuaOjKKq0EGcYzacFQ0uR1za3U89hwsgmxhI4t8G4eAtjQ+YghZMPTgwO94rD5WZ/UT0hEfnEByeQETaIozHCkklzOsm02/ncbOqy3deszf8C6TIyO3E65kFctrYvzEjIItMymdPtn2ExfhW9AlDW0HreQu8rW0q2UNxUzD0T7/G2qH3GKz5yKeUnUsqxUsrRUsr/9MaY/eFk/UnOWs/6JAg/pSMUcVZ6JEJAsH0G+Y0nOGs96/W5fMX7R/cgdI1MjZ4d0Gp+FqOe27Pm4XaG8OGpz/ze0bw7yq2tnK5sQBpPMT953uBpWdYdHVFA1zfbOGA0Uq7VInW+71rvdDvZX7MDZ/MEFo1P9Olc/kCjEdyUtpIGexWjRxVyqKThfHanyy0pa+ifVf768deJN8ezKDVwi/hDK6K/Bz4v+Byt0HLtKO8XgYoJMRAcpCU8OIisxFCKisciELx/8iOvz+UrPju7CYC7Jl0XWEGARePjMdgnUdJ+gJKGwNev2XKqBmk8i4u2QZXN2S0dUUDX4Wk9tzokhpIrf+vzhsc7SvZil02YnZOZkhrm07n8xbXpC4kIiqPVtBmHS3KgqOH8vuK61j4nXZ2sO8nuit3cNf4udJrA3akMC0W+qWQT0+KmEWH0fhEoIcR5q3xuRjQNTcEkGibxWeG/hkRj5nani7O2fegcKUxLCny2YnyYiSuirwRNO68dCnwLsx15NegtJ9Fp9MxOGJy9J7uQs5LUHxwhWp/JX0zpvNU2u9+ugP7ycd7nSLeOKVGziDJ7r5tUIImzmLgydjll7UeJCK9md0Ht+X1tDhdVfexB8MaJNzBqjdw+5nZfidonhrwiL20u5XT9aa5O9l00RkKYEZ1WMDU1HJNei2yeRLmtmLyGPJ/N6S0Ol5Xj0J0l1TRtUJQc1WoE37ziOqTLwBcF6y87SsAbtNpdHCqxYgo7xYxBHHZ4IRqN4MaM69GaSvns5GFKfdi2TErJ1rLNuFoyWTA22evdpAKFQadlccoygjRGwhO2cazM03DiHH0JRaxrq+Pj/I9ZNnoZYYbA3qkM+XdlU/EmwLctlXRaDckRJvRaDTPSIjhbnIFADLowuu54I3cdQkgWpwUm7LA7spOiCCeHGvcBTlY0BEyOExWNlLWU4NRWBryJRH+5Y/xNgKDIvoPdZ2t9tt6wt/wIza4qNK3ZzM/0fRNhfzIqIooF8SuoYTfCeIa9hfXn91ltDqy23ht5/OPYP7C77Zdd18mbDAtFnhGWwajQUT6dJznCkyA0d3Q09nYzkbqxbChe79M5B4qUkr3VO5CuYO6YNHjio0MMOq5JWYjQtfC3LzcFbNFz44kqdCEnAIacIh8VnkimZRL60EN8fqyCch+1LXvv5EcgNYyzzCEhPPD12b1JjMXAovhVRATFEpL0EbvPds0P6c0qz6vP4+WjL3Njxo1khAc+0mlIK/ImexN7K/ZydYrvrc1zCUKjY8zEWQw4rNkUNuVRaC3y+dyXS0NrO/XyMKEyi9iQwfUlvG/KEpA6dlVtprLJ/x3inS43XxbUYQw9RXJI6qCqdthXbhp9AxpDNdsLD3Os1Or1NRu708nG0n/haB7HvIxRg8I1500sRj0WYzC3pHwXt76cQsc6apu/8o1XNbXRar+4dLVbuvnlzl8Sog/h0RmP+lPkHhnSinx72Xac0nnJ5srewpO2L5ibGU1Zmaep6kd5//LL3JfDmmN7QdvM5KhZgy6lOj0qmjj9JFp1h9h0ssrv89c0t3OkvBphymdBytCyxs9xy9ilCDS4zQf49EiF15uEf352GzZXPTRfwZKsoZvN2RvRIQYmRcwnPXgqhpgv2Hr2q7BiKaG4m1rlq0+u5mD1QX4848dEGiP9KW6PDGlFvql4ExGGCHKic/wyX5hJT1iwnjkZUeCKwCLSWT+I3Suf5G8E4I6swVWkCjyLnjdkXIsmqJ73Du+hsc1PjYVzV8Mz2cQ9k8AvDD9CCueQc6ucI8oUxRUxszFFHmDdiXJOVXq3MueHp9cgXUamRM09H7k13IgOMSCEYFXGwwiNg+0N/xen+6viWaUXJAhVtlTyx/1/ZHbCbG7OuDkQInfLkFXkTreTrSVbuSr5KrQa/93ypUYGE2kOIishlJa6ieRZj1H+x2wIQDW63nC63OQ370NjT2bOqPRAi9MtKyYuASk4Zt3BiXI/xJTnrvYUmbIWI5AcM9sxuSVXVA2d5K4L+drEVbg1jdh0Hl95lZfcVHW2JvZWb8HRmMPCcYmEGod2NmdPRJqD0GoEsaYUsgz34DQe5bljP6XN5bHEXa6vEoTOWM/wnXXfwel28uTsJwdV8tiQVeQHqg7QaG/0a6dq+KqD0PzMaGbUtwCwwV0PAahG1xuna6pp054lyTAVU9Dg9G2mhsWSas4C82E+OFCK3enbeGjWP+0pMgVIYGuwiTmtrQRt/I1v5/UhC1OvIsoQiyVmL58freRURZNXFo8/PPUZLtox22cyd3T0oFJa3kSrEUSYPSV57xi7irayOyhqPczzJ35Eg70aKSVFdTbW5q9l1cerqGur40+L/kRKaMolRvYvQ1aRby7ejF6jZ27iXL/O60kQMjE5JZxf8gmZdjtfBHe67RwkPSlfz12HEG6uSh7ERaCAmzOXojVWsi4vl9IG73c070Kn4lLHg/RU6HRcbWsdlK3n+opWo+W2MStwGk5S2VrCzvzabv26fSZ3NfKZLHbt+inxDjcPhzaQNMyiVS4kqkORh5n0ZJoWEFTzdcpbC/jlobv48b7reezLO3hs22OMjxzP6ptWD8rEsSGryLeVbgtY7ejEcBPGIC2JopbFLa0cMBqo03S6lIFUDB0+YM3JnxPiknzdWBM4WfrALWOuBwRWzT4+O1Lp22zZTsWl1pmD0UjJNbbWQdl6rj/cNWEFGrSExe5l7eFy8qubL+/upsP1VN1czm6jgeXNTdxT/QfC8z/0usyDiRjLV9mqs9KjqK0ew8rE37E85TtcHXc748Omc8uob/G3JX/zalE+bzIkFXl5czn51vyAlRzVazUkhploMcaz0GbDLQSbg/1bja5bOr6I0lrMdpORua02Yjc+OihcPT0RHxLLhPDJGMIO86+j3o+86MKiJz1FpoB1wcFMb2snQmsYlK3n+kNMcAzzk65GG7aPgjorO/JqOVNzGQufHa6nty0hSGBZcws6VxtiENxh+hKjXnu+ouO0UeHoNIIzpaEsiF/BzSkPcFf6j7k6dhWNNh+7/gbAkFTkW0u3AoGtHZ0SaeLs5B+SZteQ6HCy4Zwi1/u+Gl2PdHwRT+v1VOl0zG9tQwwSV09v3Jx5PQRVcrjqJHsL6i99wuWSs5Li+b9lhy6Gs0F6FrsNnlZ0Pi465Q/umbgKu2wiLuEU7+8v5Wx1C9bWfkYCWUtoEYI3Qy0ssrWS6nSe3z7cibF43CvBQTomJYWxp6DuorWGwgF0EPI1Q1KRbyvdRqI5kfSwwEVjBAfpcGXfwUcpP2FGi2SHyURzaHJgFUPHF25bsKez0bzWti7bByvXZ1yHQIMuNJePc8uo92GX+LfbZnO/wdMbfOF964eFEgeYlTCLRHMK5uid1Nna+eJYJbklDbQ7L05o6Ql3aBLvWEJo0mr4RufKlEPc9dQXokO+cq/MTI/E2qmf5znqmu1d6rEMJoacIne4HOwu3838pPkBX0lPjQzGeMUq3ml+CLtG8OFi35cU7ZWOL9w2k4mx7XZiXa4u2wcr0aZopsRMwxx5lM2nqjhR4ZtQxAabnd1n6zCEHWVCRPag9XdeDhqh4ds5D1DtyCMz7SxrD5dT1djO4RJrn6JYpJScmfIIfw8LZVZrG5PsHT+mgbzD9CNhJj06rUef5CSHXdTP8xyFtYPTKh9yinx/1X5sTtugaMkVaQ4iNtTI9LhpSFcw6woDnBy06Eka9MEcMBq4srWjIt4Q+SLemLEUh6aCVlHGPw+W+cTyKahp4UjVWTCUsjQ98LXZvc3yzGWkWTJwhK7F6XLy4YFSGmwOTlf17i+XUnK0rJE3NBpqdFpubRBIBDIsZdi4ni6FEOK8VW7QaZmaGt6ln+c5KhvbzjehGEwMOUW+rXQbeo2eWQmzAi0K4LHKrx4Th7NpAofqdlLd3BI4YXJW8uqYu3AKwdW2NhhCX8TFoxajQUNs/Ak+P1ZJ/iWUT39xutx8fqwSl+kwANeOWuzV8QcDWo2WH854hDpHKdnjT7A1r4Y9Z+sorrNxoqKx27rl55R4WUMLnxS/ias1iaOT/8nxB4sQjxwZEp8dbxEVEnT+8az0KGx2F0fLut4dStm3Erf+ZkCKXAhxhxDiqBDCLYSY7i2hemNb6TamxU0bNLWj40ONjIu3ECan4cTGF2d2BkwWKSUftrUgncEEf+MUDKEvYpQpiunxM9BYDlLX0s7aw+XdFiy6XKqa2tlyuhpj2FHSQ8cMuoQOb3F18tXkRE+hWvcxo2P0vLKzgNL6VkrqWtmZX0u51dP9ptXuorqpnSOljVRY29hR9Rkt7goiHEuZNiqCUVGD4/vlTzo3zZiQYCHEoGP32dqLjiutb/V98lo/GahFfgS4DdjiBVkuSUVLBXkNeYOqJZdG4+kgdE3KPKQ7iLX5nwfsTa63tVPtPITZnU1alCUgMgyEWzKX0+SqIDamlE+PVHC6sunSJ/WRI6UNHKsqBmPhsLTGzyGE4MczfkiTs46siQcx6bX8eVMeNrsTu9PN0dJGNp6sYnteDYeKG6hsbKPcVsz7hX/G2ZLO17KuJzkyeMg3WL4cgnQawoL1AOg0nt4Dh4qtF7lSXG45sKQrHzAgRS6lPC6lPOktYS7FYAg77I6kCBPzx8TjbhnHMesOShsC417554mdoG1hUsQcDLrBmZbfG4tHLcasDyE28RAl9a2sP1F1yeL+fcFmd/LpkUp0ofsByS2Zg6fYkS+YEjuFa1IWsaX6TW6a2Uxts53nN+WfD0d0d7IzWh3t/G/uL3C7tFwb/QgTEyNIjzYHSPLA0yV6JS0Su8vNweKGi44rrrPh9HGLvf7gNx+5EOJBIcReIcTe6urqS5/QDSfrTpJgTiAjLPCF3Dtj0GnJiLaQbpqNU1j5Im93QPp5fnx6PVJqWDkIqx32BZPOxI3pN1Dm3E242cknh8s5WTnwCJaiOhtb86oJjtrHpKhpw9at0plfz3+alJA0Pqv5b26eIcmraubnHx5h08kq3FLickuqm9r5793P0K4tYkbIt1mWPZFRUcFD0gjwFp395KNjQ4g0B7H77MXRK06XpKzB/3X0e+KSilwIsU4IcaSbv+X9mUhK+aKUcrqUcnpMTMxlCfvz2T/nnZvfCXjYYXekRJq4KXMR0q3jo/zPqPNhLHR3tDlcnG35Ep19NLPTB3e4YW/cNuY2HG47E8fkc7qqmW2na6gcQPebVruLjSeqqHeewKWt4Y6xt3lR2sFLaFAof13yAiH6EPa0/Q+PXB/NqKhg/rG7iB++c4jvvb6HJzc/j9WwjvSga7l70o0E6TSkDtNytX3FYtARpPOoRY0QzEyL5GiZtdsoqqI6W8C6W13IJRW5lHKxlDK7m79/+kPACwl0k9OesBj1zEpPxOicQEHbLs5eTor0ANhdlIdDV8Yo03QsQ9i/ObH0CGOdElfjX9hpfBjr7jc4OYCKfvnVzWw5VYMxch9GbTBLM4Zf2GFPxJnjePG6v+CSDl4reoSkzDUsmVFNcvIpIsc/izFuLaNMU/nOpP8AYGycZdg0V75chBBdo1cyInFLuvTzPEebw0WFj1rs9ZeR/a55mdTIYKZFXQ26Bt49vMOv8aavH/Y0gl6afs2gvGPpE7mrER//gNus9RwzBNEYZOUnzuep2PrqZdUOaWxzcKa6mX3F5Wgth7k2dQkm3fCu5HchYyMzeWHRi4wLu4Lchm3saP4/lOhfJMxo5Ftjfs0Psv4Hg9bAxMRQ4sOMgRZ3UBDTyU+eHG4iMdzYbXIQeHITAuFGvZCBhh/eKoQoAeYAa4UQg7+tvA+JMgdx+4TrQGrZXLaeYj/Fm7a0OzlctxNpj2b5pMl+mdMndNSKubHZhl5K3g8JIVjYmV/8PMfLmvrdNOF0ZTNrD5cjzQeRws6d42/3keCDmNzVTH1zFa/sfZVN5Y08Hn4rX898ih9nv0hW+Gw0GkF2UhiJw7xUbX+IMAdxzhYSQjArPYq86uYu/TzPYbO7qPJlobc+MtColQ+klMlSSoOUMk5KucRbgg1FhBBkJ8QTrc2mUbOPXWdqu03C8DYnKqto0hwnWjOVOMsQ/kJ21IQJd7tZ3GLjoxAzTUIQL2v59Eg5x8oasdmdfRqqprmdUxVNrD9eRUTcQVJDMsiJ8U9LwEHDBR2RzC2l3Hn4RW5pt5IYZiY1KpipqRHEhSpLvDN6rYbwjjBE8ESvAN0uegKcrQlgEmAHyrXiZRJCjSxIXoQmqIF/Ht9DSX2rz+f8+6G1COFiYcpitIOsyXK/6FQT5n5rI01aDW+EWajVxvD5sUryqprJLbHiuoS/3GpzcKTUyvsHStCaymjVnOHWMbcMXZfT5dKpI9I5hLOVjEN/YFJyGGPjLESag3o4eWTTOQwxxmJgdIy5R0Xe3Ob0bfnlPqAUuZfRaAS3jlsCUstR61aOlF5a8QwEq83Bl9WbkI5w7p4yeBKlLotFT3pqwwAT7Q4WtNh4NTSU45O/T6hRzwub86mwtrG/qJ6W9u4t8/oWO/uL6jlZ0cSXBfUkjNpMsC6ElSPRrdJT1ctBXg1zMBDVSZEDzE6PorShtcdEoILawFrlSpH7gAlx8aSbJ6MJyeWTw2Xnm7f6gmOVlTSJo8RpZ5AUMcRDx3JWemrDhKUAgu84TTRqNWyP0fCdqzOotzl4aftZ6lvs7D5be36hSUpJm8NFZWMbB4rrcbrcvP1lMaFhZdTKg9wz4d8IDQoN9KvzPz1VvRzk1TAHAyEGHUb9V/H009Mi0Ah6XPS02hx+DznujFLkPkCv1XB9xlI0QXVsKtzL8fJGn8SbSil5+cBahMbFwpRru3zwhiw5Kz01Yp5qIOvhI1yZdCVrC98iNUbLndNTyC2x8umRCtxuyKtqZtOpatYfr2Lb6RoOl1hxuiRv7CniTE0LMambsOjD+Makfwv0qwoMne5wzjNEqmEOBjqHIVqMerISw9hztg53D1Eq/g457oxS5D7ijvE3ohNBuM17+fRIBWVW71vl1c3tHKrbDM5w7syZ5/XxBwPfnfxdrHYrJ22fcc24GGamRfLBgVJe3VlAm8NF9Jl/Mu/jBSxaPY55Hy3g+Gd/ZePJauZMsFLlzOXr2V/HrB+hKecX3OEMpWqYg4HoC9wrs9IjqbPZyeuhMmd9i8OnTVF6Y+hmjgxyos2hzIpbwE73Vr44XsIN2fHEhxq9mnCxp6CUFu0xEjWLSI4YnspqUswk5iXN45281/jdnGv5+rw0Is1BfHasgpSSj1kiXkTv9oQlmlrLeMD2v0RlPMq7loOE2yO5Z+LXAvwKAkzOSqW4L5NIcxAazVe1aaakhBOk07D7bB1j47ovSne2toWIACwgK4vch6wcfytu0Uqb/jDrjld5NUypvsXOO8c+R2hcLE1fMjzcKj3w6IxHsbvs/N9jTxFu1rLiimQeWzqeh+Qb55X4OYKFHVPby+Q35fLgpAdGXAKQwntoNYLw4K+UslGvZWpKOF8W1PVYMKuu2U6Dzf9WuVLkPuTqlDlEGGIIjz3EZ0cryK9u7nMc9KUoqG3haOMWhCuc27PmeGXMwUpGWAa/mPMLDlQdYGvNq+h1GkbHhBDPxbWi9xkM/Geohmmx01k1/s4ASKsYTkSbL3av2OwuDpdaezznTADiypUi9yFajZYbM27CHnQcq72Oz45Wcrpy4AsiTW0Otp8tpE13nNSg2SSEDU+3SmduzLiRlWNX8trxv9OmzyXCHERbcEKXY4p0Ov4jLppENzy78I/otfoeRlMo+ka0paubZGJiKBajjl09xJSDxyr3Rvnl/qAUuY+5Y+wtSNyMGnWSTw6Xc7qyqdtU3/5QWGvjg9MfIDQu7su583y1tuHOozMfZULkBJ7Y8VN21b1B5dwf4tIacQMHDUH8e1wMEsHzkx4atMXVFEOL4CAdwUFfuS09DSciOVTc0Ovd9eXUBhoII0MDBJCM8AwmRGahCd2L0+3mw4NlHC1rpN15eQW1bHYnucV1VMhNhDKOK0dle1niwYtBa+DZhc8yP2k+L+S+wNeKX+LJKYtZkprCvYnxVOp1/HH8/aTO+E6gRVUMIy5KDsqIxOmW7C9s6PGcWj9b5UqR+4EVY2+jur2AGeOsbM+rIa+ymSOljf2umuZ2S46VNfLOsY1oguq4LuUWokNGVop1vDmePyz4A6tvWs0VcVfwufUU40ddw2/m/4YNX9vF9Lk/DrSIimFG1AXfsfQoM7EWA7u66efZmXw/WuUq/NAP3Dz6Zp7d/xxu40bMhhW8tbeIlEgT+dUtZMaG9HmcMzXNFNbaOGn7HEOIhVvGLh2x9aMnRE3guYXPBVoMxQggIjgIrUacL7UhhGB2RhQfHSqjrsXeY72acxEsnSNffMXI1AJ+xqQz8bUJd3G8cReLJklOVTaz8WQ1BTUtfS7NWtPcTkGNjbXHTqAJOc70qCWMiQ33reAKhQKtRlwUGz4rPRIJ7L6UVV7tnwgWpcj9xKrxqzBojbQEr2dSUhir9xZTWNvC4RIrBZcIV2pzuDha1khtczu7qj9BCDd3jr+D4CB1Q6VQ+IOoCxR5XKiRjGgzu3qovXKO+ha7X7I9lSL3E5HGSG7JXM6+2vWsmGnBYtTxly1nsLW7OsqzNlyUZOB2S2p3/gOeyeaqN8Yw59OFBIdtJT14GjNTxgTolSgUI48L0/UBZmf0XhHxHPnVvveVK0XuR+6beB9u6SK3aS0PXJlBTXM7r+0qREpJVWM7O/JrOVBUz+nKJopqbeStf4nwdT/EaCtDINlgaaNd18b95nRCjSpGWqHwF6YgLcGGrtnTM9Ii0ArBrvze3SsNNgc1Aww5vhRKkfuRlNAUFqcuZnvlGpKi3CyfksSegjr+tv0sDpcbu9NNbbOdwlobpyqbSDnwe7Qujw+9TqPhLxFhXGlrZfmJdwL8ShSKkUfMBVa5xahnUlIYu87WXbK6aX5Vs097ew60Z+fvhBAnhBC5QogPhBDhXpJr2PKdyd+h3d3OZxUvcEN2PMunJLLrTB3//a8T1F9Qo8FoKz//+PmIMFqF4Ed19WgbS/0ttkIx4rkwnhxg9uhIrK0Ojlc09npuk4+7CA3UIv8CyJZS5gCngJ8OXKThzZiIMTyY8yBby78gr2UXN+ck8u8LRlNubePpj4/xyo4C1h2vZNeZWipFNACn9XresYSwsrGZDIdTNQZQKAJAuEmPVtu1XeDk5HBMei07z/TuXgHIq/adVT7Q5sufSynP5anuApSGuRS5q/nWhj8zod3O20d/TkjBaqamRvCz6ycwKjKYg8UNvPVlMX/ddpY/8TXaNUZ+HxmO2S35XoNVNQZQKAKERiOIvCAmXK/VMCMtgv1FDbQ5es/WtrW7qGjsW7hxf/Fm/No3gLd72imEeBB4ECA1NdWL0w4hOrqa6x2t/MqmZ1VSPO8XPMt9WhOk3Mx/LB6LlBJrq4Pq5nbSIqfy+Ikz7Gg9xKO19YRbkjxKXNWXVigCQrTFcJGLZE5GFFtO13CgqIE5o6N6Pb+nXrMD5ZKKXAixDojvZtfjUsp/dhzzOOAEXu9pHCnli8CLANOnT/ed138w06mr+TiHgwcbrDwfEY6u4I8sHHUduA0I4amBHGrS8W7hs+xsPcTipBV87Z4nYIRmcSoUg4UL48kBMmNDiA4JYueZ2ksqcl9xSUUupVzc234hxP3ATcAi6ctl2eHABd3LH2xoRCL4S3go+49+m/syH0O6zNS1V/BlzRfsr9vAysx/4/E5P0SjGdxK3OFwUFJSQlubb24dFX3HaDSSnJyMXq9CVL2NUa8lxKijue0ry/pcyv7aw+XU2+xE+CEl/0IG5FoRQiwFHgWullL2HhWv8CxSWovPP9UC32uwMlsbyk9D3Pzm4ENdDv9Oznf53pTvIoRgsFNSUoLFYiEtLW1IyDtckVJSW1tLSUkJ6enpgRZnWBIdYuiiyMHjXvk4t5xdZ2q5PjuhhzN9x0B95H8CDMAXHV/eXVJKVUO0JxY9CR89fN69AoDexLSrn+Sd8Uv5OP9jLEEWkkKSSLGkEBMcEzhZ+0lbW5tS4oMAIQRRUVFUV1cHWpRhS3RI0EVlNeJCjYyOMbMzv5alWfF+/x4MSJFLKTO9JciI4Nwi5fqnPW6WsOTzi5ehwNcmDO1GwUqJDw7U++Bbwkx6dFqB09XVkzx3dDSv7SqksNZGWrR/u3apqkv+RnU1VyiGNEIIokMMVFi7rgfNSIvgzT1F7DhT63dFPrhX0BQKhWIQcmGzCfC0hZuSEs6es3UXFcDzNUqRKxQKRT+JMl+crg8wd3QUze1ODpda/SqPcq0ovM4vPzrKsbLea0/0l4mJofzi5qxejykoKGDp0qXMnj2bHTt2MGPGDL7+9a/zi1/8gqqqKl5//XWysrL4/ve/z5EjR3A4HDz11FMsX76cgoIC7r33XlpaPItYf/rTn5g7dy6bNm3iqaeeIjo6miNHjnDFFVfwj3/8Q/mhRzhBOg1hwfqL+nJmJYYRatSxI7+WqakRfpNHKXLFsCIvL4933nmHl156iRkzZvDGG2+wbds21qxZw29+8xsmTpzIwoULeemll2hoaGDmzJksXryY2NhYvvjiC4xGI6dPn+auu+5i7969ABw4cICjR4+SmJjIvHnz2L59O/Pnzw/wK1UEmihz0EWKXKsRzMqIYsOJKpraHFj8VG5aKXKF17mU5exL0tPTmTRpEgBZWVksWrQIIQSTJk2ioKCAkpIS1qxZw+9//3vAEzZZVFREYmIiDz30EAcPHkSr1XLq1KnzY86cOZPkZE8ZoSlTplBQUKAUuYJoi4Ez3bRymzc6ii+OVbL7bB2LJ8T5RRalyBXDCoPhK9+lRqM5/1yj0eB0OtFqtbz33nuMGzeuy3lPPfUUcXFxHDp0CLfbjdFo7HZMrVaL0+mbehmKoYXFoCNIp8Hu7LqwmRwRTGpkMDvya/2myNVip2JEsWTJEp577rnz5UQPHDgAgNVqJSEhAY1Gw2uvvYbL1XslO4VCCNFt9ArA/MxoiupsFNf5J+FdKXLFiOKJJ57A4XCQk5NDVlYWTzzxBADf+973+Pvf/87kyZM5ceIEZrN/44AVQ5MLuwadY2ZaJDqNYHt+jV/kEIGoczV9+nR5biFJMTw4fvw4EyZMCLQYig7U++EfnC43W05X4+4mbPz/bs7nZEUTv1+Rg66jcmladDCZsZbLnk8IsU9KOf3C7coiVygUistEp9UQZurevTKvI6Y81w8x5UqRKxQKxQDoyb2SlRhGmEnP9jzfu1eUIlcoFIoB0NOCp1YjmJMRxeFSK9ZWR7fHeAulyBUKhWIAmA06goO03e6bOzoKt4RdfWjOPBCUIlcoFIoBEtWDeyUx3MToGDPb8mrwZWCJUuQKhUIxQKJ7cK+AJ6a83NrGmZqLs0C9hVLkisCQuxqeyYanwj3/c1f7ZJqCggKys7N9MnZ/OHjwIJ988sn552vWrOG3v/1tACVSeJOI4CC0mu4Lqc1Ii8Sg07DttO8WPZUiV/if3NWelnfWYkB6/n/0sM+Uube5nBT9CxX5smXLeOyxx7wpliKAaDSCSHP3VrlRr2X6qAj2FNTRavdNxvCAFLkQ4ldCiFwhxEEhxOdCiERvCaYYxqx/umvfUvA8X//0gIf+wx/+QHZ2NtnZ2fzxj38EPIr37rvvZsKECaxYsQKbzZM2/dhjjzFx4kRycnL40Y9+BEB1dTW33347M2bMYMaMGWzfvh3w1GK59957mTdvHvfeey+zZ8/m6NGj5+ddsGABe/fuZc+ePcyZM4epU6cyd+5cTp48id1u58knn+Ttt99mypQpvP3227zyyis89JCn2XZBQQELFy4kJyeHRYsWUVRUBMD999/Pww8/zNy5c8nIyODdd98FoLy8nKuuuoopU6aQnZ3N1q1bB3zdFAMn2tK9nxw87pV2pyd5yBcM1CL/nZQyR0o5BfgYeHLgIimGPdaS/m3vI/v27ePll19m9+7d7Nq1i//3//4f9fX1nDx5ku9973scP36c0NBQnn/+eWpra/nggw84evQoubm5/PznPwfgBz/4AY888ghffvkl7733Ht/61rfOj3/s2DHWrVvHm2++yZ133snq1Z47iPLycsrLy5k+fTrjx49n69atHDhwgKeffpqf/exnBAUF8fTTT3PnnXdy8OBB7rzzzi5yf//73+e+++4jNzeXu+++m4cffvj8vvLycrZt28bHH3983oJ/4403WLJkCQcPHuTQoUNMmTJlQNdN4R2ierDIATJjQ4gLNfDpkQqfzD0gRS6l7Nw9wAz4P99fMfQIS+7f9j6ybds2br31VsxmMyEhIdx2221s3bqVlJQU5s2bB8A999zDtm3bCAsLw2g08s1vfpP333+f4OBgANatW8dDDz3ElClTWLZsGY2NjTQ3NwMed4jJZAJg5cqV5y3k1atXs2LFCsBTfOuOO+4gOzubRx55pIvV3hM7d+7ka1/zNN6+99572bZt2/l9t9xyCxqNhokTJ1JZWQnAjBkzePnll3nqqac4fPgwFsvlp3wrvIdRr8Vi7L6grBCC+ZnRHClt5Ex1s9fnHrCPXAjxn0KIYuBulEWu6AuLngS9qes2vcmz3Qdc2M1HCIFOp2PPnj2sWLGCjz/+mKVLlwLgdrvZtWsXBw8e5ODBg5SWlhISEgLQpZBWUlISUVFR5Obm8vbbb5+3sp944gmuueYajhw5wkcffURbW9cGvf2lcwndc+FrV111FVu2bCEpKYn777+fV199dUBzKLxHb+6VuaOjGRsXQr3N7vV5L6nIhRDrhBBHuvlbDiClfFxKmQK8DjzUyzgPCiH2CiH2Vlf7xk+kGCLkrISbn4WwFEB4/t/8rGf7ALjyyiv58MMPsdlstLS08MEHH3DllVdSVFTEzp07AY9bYv78+TQ3N2O1Wrnhhht45plnOHToEADXXXcdzz333PkxDx482ON8d955J//zP/+D1WolJycH8FjkSUlJALzyyivnj7VYLDQ1NXU7zty5c3nrrbcAeP3117nyyit7fZ2FhYXExcXxwAMP8K1vfYv9+/f3fmEUfiO6h3hygDCTnufvnsYVoyK9Pu8lFbmUcrGUMrubv39ecOjrwO29jPOilHK6lHJ6TEzMQOVWDHVyVsIjR+CpBs//ASpxgGnTpnH//fczc+ZMZs2axbe+9S0iIiIYN24cf/7zn5kwYQL19fV897vfpampiZtuuomcnBzmz5/PH/7wBwCeffZZ9u7dS05ODhMnTuSFF17ocb4VK1bw1ltvsXLlV7I/+uij/PSnP2Xq1KldoluuueYajh07dn6xszPPPfccL7/8Mjk5Obz22mv87//+b6+vc9OmTUyePJmpU6fy9ttv84Mf/OByLpfCB4QaPc0m/M2AytgKIcZIKU93PP4+cLWUcsWlzlNlbIcfqmzq4EK9H4HjWFkjZQ2t3e7zVRnbgbZ6+60QYhzgBgqB7wxwPIVCoRjSRFuCelTkvmJAilxK2aMrRaFQKEYikcFBaDR022zCV6jMToVCofAiOq2G8OCeY8p9gVLkCoVC4WV6ajbhK5QiVygUCi/TWxiiL1CKXKFQKLyMKUiL2TDQWJK+oxS5QtEHPvzwQ44dOxZoMRRDiBiL//zkSpErFH1AKXJFf/Gne8V/tr9ixPDfe/6bE3UnvDrm+Mjx/GTmTy553D/+8Q+effZZ7HY7s2bN4hvf+AYPPPAAe/bsweVyMXPmTN5++23S0tJYvnw59fX1OBwOfv3rX7N8+XIAXn31VX7/+98jhCAnJ4fvfve7rFmzhs2bN/PrX/+a9957j9GjR3v19SmGH2EmPXqdBofT93GISpErhg3Hjx/n7bffZvv27ej1er73ve9x8uRJli1bxs9//nNaW1u55557yM7Oxul08sEHHxAaGkpNTQ2zZ89m2bJlHDt2jF//+tfs2LGD6Oho6urqiIyMZNmyZdx0003nqxwqFJdCCEF0SBDlDQMrnNYXlCJXeJ2+WM6+YP369ezbt48ZM2YA0NraSmxsLE8++SQzZszAaDTy7LPPAp5Kgj/72c/YsmULGo2G0tJSKisr2bBhA3fccQfR0dEAREZ6v8CRYuQQE2JQilyh6A9SSu677z7+67/+q8v28vJympubcTgctLW1YTabef3116murmbfvn3o9XrS0tIGXHJWobiQSLN/sjzVYqdi2LBo0SLeffddqqqqAKirq6OwsJBvf/vb/OpXv+Luu+/mJz/x3C1YrVZiY2PR6/Vs3LiRwsJCABYuXMg777xDbW3t+TGg9zK0CkVP+CvLU1nkimHDxIkT+fWvf811112H2+1Gr9ezfPly9Ho9X/va13C5XMydO5cNGzZw9913c/PNNzNp0qTzLdoAsrKyePzxx7n66qvRarVMnTqVV155hVWrVvHAAw/w7LPP8u6776rFTkWfiQkxUNfs/WYSnRlQGdvLRZWxHX6osqmDC/V+DB7aHC62na4BfFfGVrlWFAqFwocY9VpCeujl6S2UIlcoFAofE9NLL09voBS5wmsEwk2nuBj1Pgw+fJ3lqRS5wisYjUZqa2uVEgkwUkpqa2sxGo2BFkXRiVCjDoPed+pWRa0ovEJycjIlJSVUV1cHWpQRj9FoJDk5OdBiKDrhyfL0nVWuFLnCK+j1etLT0wMthkIxaImxGGiw+SYM0Su2vhDih0IIKYSI9sZ4CoVCMdyIDA5CI4RPxh6wIhdCpADXAUUDF0ehUCiGJxqNIMpH7hVvWOTPAI8CapVLoVAoeiHUR/HkAxpVCLEcKJVSHhKXuGUQQjwIPNjxtFkIcfIyp40Gai7zXF+i5OofSq7+oeTqH4NVLhiYbKO623jJFH0hxDogvptdjwM/A66TUlqFEAXAdCmlTy+eEGJvdymqgUbJ1T+UXP1DydU/Bqtc4BvZLmmRSykX9yDMJCAdOGeNJwP7hRAzpZQV3hRSoVAoFD1z2a4VKeVhIPbcc39Z5AqFQqHoylDM7Hwx0AL0gJKrfyi5+oeSq38MVrnAB7IFpIytQqFQKLzHULTIFQqFQtEJpcgVCoViiDMoFbkQ4g4hxFEhhFsI0WOYjhBiqRDipBAiTwjxWKft6UKI3R3b3xZCeKVpnhAiUgjxhRDidMf/iG6OuUYIcbDTX5sQ4paOfa8IIc522jfFX3J1HOfqNPeaTtsDeb2mCCF2drzfuUKIOzvt8+r16unz0mm/oeP153Vcj7RO+37asf2kEGLJQOS4DLn+PyHEsY7rs14IMarTvm7fUz/Jdb8QorrT/N/qtO++jvf9tBDiPj/L9UwnmU4JIRo67fPl9XpJCFElhDjSw34hhHi2Q+5cIcS0TvsGdr2klIPuD5gAjAM24YmE6e4YLZAPZABBwCFgYse+1cCqjscvAN/1klz/AzzW8fgx4L8vcXwkUAcEdzx/BVjhg+vVJ7mA5h62B+x6AWOBMR2PE4FyINzb16u3z0unY74HvNDxeBXwdsfjiR3HG/CE3OYDWj/KdU2nz9B3z8nV23vqJ7nuB/7UzbmRwJmO/xEdjyP8JdcFx38feMnX16tj7KuAacCRHvbfAHwKCGA2sNtb12tQWuRSyuNSyktlfs4E8qSUZ6SUduAtYLkQQgALgXc7jvs7cIuXRFveMV5fx10BfCqltHlp/p7or1znCfT1klKeklKe7nhcBlQBMV6avzPdfl56kfddYFHH9VkOvCWlbJdSngXyOsbzi1xSyo2dPkO78ORs+Jq+XK+eWAJ8IaWsk1LWA18ASwMk113Am16au1eklFvwGG49sRx4VXrYBYQLIRLwwvUalIq8jyQBxZ2el3RsiwIapJTOC7Z7gzgpZXnH4wog7hLHr+LiD9F/dtxWPSOE8FYFnb7KZRRC7BVC7Drn7mEQXS8hxEw8VlZ+p83eul49fV66PabjeljxXJ++nOtLuTrzTTxW3Tm6e0/9KdftHe/Pu8JTQK8/5/pSLjpcUOnAhk6bfXW9+kJPsg/4egWsHrnoJfVfSvlPf8tzjt7k6vxESimFED3Gbnb80k4CPuu0+ad4FFoQnljSnwBP+1GuUVLKUiFEBrBBCHEYj7K6bLx8vV4D7pNSujs2X/b1Go4IIe4BpgNXd9p80XsqpczvfgSv8xHwppSyXQjxbTx3Mwv9NHdfWAW8K6V0ddoWyOvlMwKmyGUPqf/9oBRI6fQ8uWNbLZ5bFl2HVXVu+4DlEkJUCiESpJTlHYqnqpehVgIfSCkdncY+Z522CyFeBn7kT7mklKUd/88IITYBU4H3CPD1EkKEAmvx/Ijv6jT2ZV+vbujp89LdMSVCCB0Qhufz1JdzfSkXQojFeH4cr5ZStp/b3sN76g3FdEm5pJS1nZ7+Fc+ayLlzF1xw7iYvyNQnuTqxCvj3zht8eL36Qk+yD/h6DWXXypfAGOGJuAjC86atkZ7Vg414/NMA9wHesvDXdIzXl3Ev8s11KLNzfulbgG5Xt30hlxAi4pxrQngagMwDjgX6enW8dx/g8R2+e8E+b16vbj8vvci7AtjQcX3WAKuEJ6olHRgD7BmALP2SSwgxFfgLsExKWdVpe7fvqR/lSuj0dBlwvOPxZ8B1HfJF4OlX0PnO1Kdydcg2Hs/C4c5O23x5vfrCGuDfOqJXZgPWDmNl4NfLVyu4A/kDbsXjJ2oHKoHPOrYnAp90Ou4G4BSeX9THO23PwPNFywPeAQxekisKWA+cBtYBkR3bpwN/7XRcGp5fWc0F528ADuNRSP8AQvwlFzC3Y+5DHf+/ORiuF3AP4AAOdvqb4ovr1d3nBY+rZlnHY2PH68/ruB4Znc59vOO8k8D1Xv68X0qudR3fg3PXZ82l3lM/yfVfwNGO+TcC4zud+42O65gHfN2fcnU8fwr47QXn+fp6vYkn6sqBR399E/gO8J2O/QL4c4fch+kUkTfQ66VS9BUKhWKIM5RdKwqFQqFAKXKFQqEY8ihFrlAoFEMcpcgVCoViiKMUuUKhUAxxlCJXKBSKIY5S5AqFQjHE+f8BHU1xlouZWnsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred, = model.predict(x_test.reshape([-1, 1]), samples, [process])\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0)\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_new_train, u_new_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50cdbead",
   "metadata": {},
   "source": [
    "#### Why?\n",
    "\n",
    "It is against the intuition that more data for training could bring worse in estimate, even for uncertainty estimate. Generally, in the field of data science, it is always the case that more data we have, the better the prediction is. In the following, we show empirically one of the explanations for why it is not the case in above. The inexpressive neural network model seems to take the blame. With a larger and deeper network, everything returns to normal.\n",
    "\n",
    "We don't discuss or argue the merits and the necessity of calibrations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9e6106d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supporting backend tensorflow.compat.v1\n",
      "\n",
      "Compiling a MCMC method\n",
      "\n",
      "sampling from posterior distribution ...\n",
      "\n",
      "Finished sampling from posterior distribution ...\n",
      "\n",
      "0.471\n"
     ]
    }
   ],
   "source": [
    "# deeper and larger neural network for the model\n",
    "process = neuq.process.Process(\n",
    "    surrogate=neuq.surrogates.FNN(layers=[1, 50, 50, 1]),\n",
    "    prior=neuq.variables.fnn.Samplable(layers=[1, 50, 50, 1], mean=0, sigma=1),\n",
    ")\n",
    "likelihood = neuq.likelihoods.Normal(\n",
    "    inputs=x_new_train,\n",
    "    targets=u_new_train,\n",
    "    processes=[process],\n",
    "    sigma=0.1,\n",
    ")\n",
    "model = neuq.models.Model(\n",
    "    processes=[process], likelihoods=[likelihood],\n",
    ")\n",
    "model.compile(method)\n",
    "\n",
    "samples, results = model.run()\n",
    "print(np.mean(results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b0242b7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred, = model.predict(\n",
    "    x_test.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0)\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_new_train, u_new_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ede50eb3",
   "metadata": {},
   "source": [
    "#### Active learning, by adding one measurements\n",
    "\n",
    "Now, we move to another topic: active learning. In this case, we wish to use the predicted uncertainty to guide us for further sampling. The spirit is, we know the existing dataset is not enough to give trustworthy prediction for some region, and we want to locate the place where the uncertainty is the largest, so that adding more measurements will suppress the uncertainty to make the prediction less uncertain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3599b239",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supporting backend tensorflow.compat.v1\n",
      "\n",
      "Compiling a MCMC method\n",
      "\n",
      "sampling from posterior distribution ...\n",
      "\n",
      "Finished sampling from posterior distribution ...\n",
      "\n",
      "0.61\n"
     ]
    }
   ],
   "source": [
    "process = neuq.process.Process(\n",
    "    surrogate=neuq.surrogates.FNN(layers=[1, 50, 50, 1]),\n",
    "    prior=neuq.variables.fnn.Samplable(layers=[1, 50, 50, 1], mean=0, sigma=1),\n",
    ")\n",
    "likelihood = neuq.likelihoods.Normal(\n",
    "    inputs=x_train,\n",
    "    targets=u_train,\n",
    "    processes=[process],\n",
    "    sigma=0.1,\n",
    ")\n",
    "model = neuq.models.Model(\n",
    "    processes=[process], likelihoods=[likelihood],\n",
    ")\n",
    "\n",
    "method = neuq.inferences.HMC(\n",
    "    num_samples=1000,\n",
    "    num_burnin=1000,\n",
    "    init_time_step=0.1,\n",
    "    leapfrog_step=50,\n",
    "    seed=None,\n",
    ")\n",
    "model.compile(method)\n",
    "\n",
    "samples, results = model.run()\n",
    "print(np.mean(results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c1fd5b55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = np.linspace(np.min(x_train), np.max(x_train), 100).reshape([-1, 1])\n",
    "u_test = x_test + 1.5 * np.sin(4*np.pi*x_test)\n",
    "\n",
    "u_pred, = model.predict(\n",
    "    x_test.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0)\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_train, u_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5703197f",
   "metadata": {},
   "outputs": [],
   "source": [
    "most_uncertain_id = np.argmax(std)\n",
    "most_uncertain_x = x_test[most_uncertain_id].reshape([-1, 1])\n",
    "most_uncertain_u = u_test[most_uncertain_id].reshape([-1, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "484061e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling a MCMC method\n",
      "\n",
      "sampling from posterior distribution ...\n",
      "\n",
      "Finished sampling from posterior distribution ...\n",
      "\n",
      "0.505\n"
     ]
    }
   ],
   "source": [
    "x_new_train = np.concatenate([x_train, most_uncertain_x], axis=0)\n",
    "u_new_train = np.concatenate([u_train, most_uncertain_u], axis=0)\n",
    "likelihood = neuq.likelihoods.Normal(\n",
    "    inputs=x_new_train,\n",
    "    targets=u_new_train,\n",
    "    processes=[process],\n",
    "    sigma=0.1,\n",
    ")\n",
    "\n",
    "model.likelihoods = [likelihood]\n",
    "model.compile(method)\n",
    "\n",
    "samples, results = model.run()\n",
    "print(np.mean(results))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "564531d5",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred, = model.predict(\n",
    "    x_test.reshape([-1, 1]), samples, [process]\n",
    ")\n",
    "mu = np.mean(u_pred, axis=0)\n",
    "std = np.std(u_pred, axis=0)\n",
    "\n",
    "plt.plot(x_test.flatten(), mu.flatten(), label='mean')\n",
    "plt.fill_between(x_test.flatten(), (mu+2*std).flatten(), (mu-2*std).flatten(), alpha=0.3)\n",
    "plt.plot(x_new_train, u_new_train, 'o', label='observations')\n",
    "plt.plot(x_test, u_test, label='exact')\n",
    "plt.legend()\n",
    "plt.ylim([-4, 4])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "179fdcf8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
